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The book provides a comprehensive theory of ODE which come as Euler-Lagrange equations from generally higher-order Lagrangians. Emphasis is laid on applying methods from differential geometry (fibered manifolds and their jet-prolongations) and global analysis (distributions and exterior differential systems). Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, etc., for any Lagrangian system of any order are presented. The key idea - to build up these theories as related with the class of equivalent Lagrangians - distinguishes this book from other texts on higher-order mechanics. The...

This book is a collection of survey articles in a broad field of the geometrical theory of the calculus of variations and its applications in analysis, geometry and physics. It is a commemorative volume to celebrate the sixty-fifth birthday of Professor Krupa, one of the founders of modern geometric variational theory, and a major contributor to this topic and its applications over the past thirty-five years. All the authors invited to contribute to this volume have established high reputations in their field. The book will exclusively provide a variety of important results, techniques and...